Cos1°+cos2°+cos3°+cos4°+........................+cos180° is equals to

Cos1°=cos(π-179)=-cos179°Cos2°=cos[π-178]=-cos178°And so on.Therefore only cos180 remains which is equal to -1,So the answer is -1.

cos 1°= cos(180°-179°) = -cos 179°When we write this gorm for forst 89 terms,Then the terms with 91° to 179° are cancelled.Now we are lest with cos 90°+cos 180°=0+ (-1) = -1